Then we give an independent derivation of the pure rotational spin-averaged transition frequency based on the experimental data of the (\(G_1=1,G_2=2\) ) manifold of spin states. We keep here the notation for the spin coupling similar to Ref. [1]}: \(\mathbf {G}_1=\mathbf {s}_e\!+\!\mathbf {I}_p\) , \(\mathbf {G}_2\!=\!\mathbf {G}_1\!+\!\mathbf {I}_d\) , and \(\mathbf {F}\!=\!\mathbf {G}_2\!+\!\mathbf {N}\) , where \(\mathbf {N}\)  is the total orbital angular momentum operator.
